Question

A magnetic needle of magnetic moment $6.7\times {10}^{-2}A{m}^2$ and moment of inertia $7.5\times {10}^{-6}kg{m}^2$ is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is

• A. 6.98 s
• B. 8.76 s
• C. 6.65 s
• D. 8.89 s

Answer 1

The correct option is C 6.65 s

We know that,

time period of oscillation $=2\pi \sqrt{\frac{I}{BM}}$

Where, I is moment of inertia of the needle

B is the magnetic field

M is the magnetic moment

So,

time taken for 10 oscillations $=10T$

$=20\pi \sqrt{\frac{I}{BM}}$

$=20\pi \sqrt{\frac{7.5\times {10}^{-6}kg{m}^2}{\left(0.01T\right)(6.7\times {10}^{-2}A{m}^2)}}$

$=6.65s$

Option $-C$ is correct